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It’s snowed. And snowed. And snowed. Now, winter — as if it still has something to prove — is dealing weather-weary New Englanders a new blow: extreme cold.

Cold air from the Arctic Circle is descending on the region, with temperatures expected to bottom out overnight at perilously frigid lows predicted to reach about minus 5 degrees in Boston, with wind chill making it feel more like minus 22. The thermometer today won’t crack 20 degrees, and tomorrow will warm up a little more than yesterday’s low — 8 degrees.

But that is nothing compared to the central and western parts of the state.

The National Weather Service forecast predicted overnight lows of minus 21 degrees in Fitchburg, minus 18 in Amherst, and minus 19 in Greenfield.

The bitter cold will loosen its grip on Tuesday, but don’t expect a reprieve from winter’s fury.

A storm making its way up the coast has the potential to dump more than 6 inches of snow late that day or the next.

Yesterday, joggers, walkers, birders, and dog-walkers at Castle Island soaked up the sun and milder temperatures before the deep freeze.

Nicole Peterson, out walking with Tilly, her black Labrador puppy, said dog ownership has its downside during extreme weather.

Peterson, 35, lamented the frequent — and often early — outdoor excursions.

“It just stinks to have a dog when it’s 6 in the morning and you know its going to be below freezing,’’ said the South Boston native. “If you don’t like it, don’t live here.’’

State and city officials were preparing for the storm by increasing outreach to homeless people, cautioning people to be careful with space heaters, and monitoring highways for icy conditions.

Mayor Thomas M. Menino said that extra staff will be working to respond to “no heat’’ calls to help tenants whose landlords do not provide adequate heat. The mayor’s hotline is 617-635-4500.

The city is also opening community centers where people can stay warm during the day, and extensive efforts are being made to persuade homeless people to stay in shelters.

The fire department will be checking vacant buildings to urge people who may be inside to go to shelters. The Pine Street Inn will also have outreach teams in vans.

The Boston Water and Sewer Commission has an emergency line available for people with questions about frozen pipes, at 617-989-7000.

The state also promised help for those suffering from the cold.

“I have put state agencies on high alert to respond to any public safety and public health issues that may emerge, including contacting our largest individual emergency shelters to ensure they will be open to everyone around the clock,’’ Governor Deval Patrick said in a statement. “We are also reaching out to cities and towns to make sure they are prepared, and have pledged support, where needed, of state fuel assistance, transportation, emergency housing, and emergency management resources.’’

Officials urged people to dress in layers, cover exposed skin, check smoke and carbon monoxide detectors, not to use ovens or grills to heat their homes, and to check on neighbors.

In that spirit, dozens of high school students from around Massachusetts and New Hampshire carried bags of donated clothes into St. Francis House in Boston as part of a church service project yesterday.

“T-shirts, coats, hats, gloves, pants, we brought everything, said Alyssa Bigay, 44, of Concord, a volunteer. Bigay said the donations are part of a wider project called City Reach, run by the Ecclesia Ministries at the Cathedral Church of St. Paul nearby on Tremont Street. “The timing is actually really good, that we’re getting all of this done.’’

No precipitation is forecast until late Tuesday or Wednesday, so problems with travel are not expected.

But officials said highways, trains, and airport runways will be carefully monitored.

The MBTA will move its trains into tunnels or maintenance areas to keep them warm. The MBTA will also take a step it only implements in extreme conditions, of allowing commuter rail engines to idle overnight, according to Richard Davey, general manager of the T.

“There’s water within the locomotive systems to keep the engines cool. Those can freeze, causing havoc to the system,’’ Davey said. “Our top priority will be to protect the Monday morning rush hour, to ensure a seamless commute.’’

At the Pine Street Inn, no one will be turned away, said spokeswoman Barbara Trevisan. Cots are being set up to increase capacity.

“The shelter is open around the clock, and we encourage everyone to stay inside during the day,’’ Trevisan said. “Sometimes there are people who wouldn’t normally come in, but when the weather gets this extreme they can be persuaded.’’

“A lot of the shelters are overbooked,’’ he said. Royster, who is transgender, said his sexual orientation compounds the difficulty of staying in a shelter.

Panhandling buys cheap $1 hand and feet warmers, he said, but during the night when temperatures plummet some homeless take different tactics.

“Some people choose liquor, some people choose sleeping bags,’’ said Royster, a Philadelphia native. “Sometimes a little of both.’’

City and state officials were working hard to ensure that people were taking precautions to prepare for the bitter cold. But even as they conducted meetings and conference calls to orchestrate services for the subzero temperatures, they were starting to think ahead to the possibility of yet more snow.

“We’re dealing with the cold today — Saturday, Sunday, Monday,’’ Menino said. “As we work through that and put procedures in place, we’re also keeping an eye on the storm.’’

Emma Vigneras, a transplant from Paris, strolled through Quincy Market with two of her sons yesterday.

The winter is the family’s first in Boston after moving to the States about six months ago.

“We like it because we’re not used to it,’’ said Vigneras, whose children enjoy playing in the snow, which rarely falls in Boston-sized quantities in Paris.

“All the people told us, [winter] is long, it keeps going,’’ she said. “I don’t know if I will say the same thing at the end of it.’’